`(3)/(2)=(-(5m-3))/(3m)+(7)/(12m)`
What is the solution for m in the equation above?

Answer

To solve the equation \(\frac{3}{2} = \frac{-(5m-3)}{3m} + \frac{7}{12m}\), we will follow these steps:

### Step 1: Simplify the Right Side
First, we need to simplify the right side of the equation by finding a common denominator for the fractions. The denominators are \(3m\) and \(12m\). The least common multiple (LCM) of \(3m\) and \(12m\) is \(12m\).

Rewriting the fractions with the common denominator:
\[ \frac{-(5m-3)}{3m} = \frac{-4(5m-3)}{12m} = \frac{-20m + 12}{12m} \]
So, the equation becomes:
\[ \frac{3}{2} = \frac{-20m + 12 + 7}{12m} \]

### Step 2: Combine the Right Side
Now, combine the terms in the numerator on the right side:
\[ \frac{3}{2} = \frac{-20m + 19}{12m} \]

### Step 3: Cross-Multiply
Next, we will cross-multiply to eliminate the fractions:
\[ 3 \cdot 12m = 2 \cdot (-20m + 19) \]
This simplifies to:
\[ 36m = -40m + 38 \]

### Step 4: Combine Like Terms
Now, let's combine the terms involving \(m\):
\[ 36m + 40m = 38 \]
This gives us:
\[ 76m = 38 \]

### Step 5: Solve for \(m\)
Now, divide both sides by 76 to isolate \(m\):
\[ m = \frac{38}{76} = \frac{1}{2} \]

### Final Solution
Thus, the solution for \(m\) is:
\[ \boxed{\frac{1}{2}} \]

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